Subgroups — D₄×C₃₁×#104 #21479192

Order 7936.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#104	C₂	1	2	yes	maximal, complemented
4	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1896	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1871	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1789	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₃₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
14	C₃₁×#550	C₄	1	1	yes	characteristic, complemented
15	D₄×Q₈×C₃₁	C₄	1	1	yes	characteristic, complemented
16	C₃₁×#548	C₄	1	2	yes	complemented
17	C₃₁×#547	—	2	1	no	—
18	C₃₁×#547	C₄	1	1	yes	characteristic, complemented
19	C₃₁×#546	—	2	2	no	—
20	C₃₁×#546	C₄	1	2	yes	complemented
21	D₄²×C₃₁	—	2	1	no	—
22	D₄²×C₃₁	C₄	1	1	yes	characteristic, complemented
23	C₃₁×#532	—	2	1	no	—
24	C₃₁×#532	C₂²	1	1	yes	characteristic
25	C₃₁×#525	—	2	2	no	—
26	C₃₁×#525	C₂²	1	2	yes	—
27	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₃₁	—	2	1	no	—
29	C₂×C₄×D₄×C₃₁	—	2	1	no	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
32	C₃₁×#436	—	2	1	no	—
33	C₃₁×#435	—	2	2	no	—
34	C₈×D₄×C₃₁	—	2	1	no	—
35	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃₁×#104	—	2	8	no	—
37	C₂×C₃₁×#104	C₂²	1	2	yes	—
38	C₂×C₃₁×#104	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#104	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#104	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#104	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#104	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#104	C₂²	1	2	yes	complemented
44	C₃₁×#407	C₂²	1	2	yes	complemented
45	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
47	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
49	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
50	C₄³×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#339	C₂²	1	2	yes	complemented
52	C₃₁×#339	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#339	C₂²	1	1	yes	characteristic, complemented
54	C₂×#41×C₃₁	—	2	2	no	—
55	C₂×#41×C₃₁	—	2	2	no	—
56	C₂×#41×C₃₁	—	2	4	no	—
57	C₂×#41×C₃₁	—	2	4	no	—
58	C₂×#41×C₃₁	—	4	2	no	—
59	C₂×#41×C₃₁	—	4	2	no	—
60	C₂×#41×C₃₁	C₂×C₄	1	2	yes	complemented
61	C₂×#41×C₃₁	C₂×C₄	1	2	yes	complemented
62	C₂×#41×C₃₁	C₂³	1	2	yes	—
63	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	complemented
65	C₂²×D₄×C₃₁	—	2	2	no	—
66	C₂²×D₄×C₃₁	—	2	1	no	—
67	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	complemented
68	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₃₁	—	2	2	no	—
70	C₂³×C₄×C₃₁	—	2	2	no	—
71	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
72	C₂×M₁₆×C₃₁	—	2	2	no	—
73	C₂×M₁₆×C₃₁	—	2	4	no	—
74	C₂×M₁₆×C₃₁	—	4	2	no	—
75	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
77	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₃₁	—	2	2	no	—
79	C₃₁×C₄⋊Q₈	—	2	1	no	—
80	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
81	C₃₁×#127	—	2	1	no	—
82	C₃₁×#127	C₂×C₄	1	1	yes	characteristic, complemented
83	C₃₁×#124	—	2	2	no	—
84	C₃₁×#124	C₂×C₄	1	2	yes	complemented
85	C₃₁×#123	—	2	2	no	—
86	C₃₁×#123	—	2	2	no	—
87	C₃₁×#123	—	2	2	no	—
88	C₃₁×C₂²⋊Q₈	—	2	2	no	—
89	C₃₁×C₂²⋊Q₈	—	2	2	no	—
90	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
91	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
92	C₃₁×#121	—	2	2	no	—
93	C₃₁×#121	—	2	1	no	—
94	C₃₁×#121	—	2	1	no	—
95	C₃₁×#121	—	2	1	no	—
96	C₃₁×#121	—	2	1	no	—
97	C₃₁×#121	—	2	2	no	—
98	C₃₁×#121	—	2	2	no	—
99	C₃₁×#121	C₂×C₄	1	2	yes	complemented
100	C₃₁×#121	C₂×C₄	1	2	yes	complemented
101	C₃₁×#120	—	2	2	no	—
102	C₃₁×#120	—	2	2	no	—
103	C₃₁×#120	—	2	2	no	—
104	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
105	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
106	C₄×D₄×C₃₁	—	2	8	no	—
107	C₄×D₄×C₃₁	—	2	1	no	—
108	C₄×D₄×C₃₁	—	2	2	no	—
109	C₄×D₄×C₃₁	—	2	1	no	—
110	C₄×D₄×C₃₁	—	2	1	no	—
111	C₄×D₄×C₃₁	—	2	2	no	—
112	C₄×D₄×C₃₁	—	2	1	no	—
113	C₄×D₄×C₃₁	—	2	2	no	—
114	C₄×D₄×C₃₁	—	2	1	no	—
115	C₄×D₄×C₃₁	—	2	1	no	—
116	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
118	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
120	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented
121	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
122	C₄×D₄×C₃₁	D₄	1	2	yes	—
123	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
124	C₃₁×#117	—	2	1	no	—
125	C₃₁×#117	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
127	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
132	C₂×C₄²×C₃₁	—	2	1	no	—
133	C₂×C₄²×C₃₁	—	2	1	no	—
134	C₂×C₄²×C₃₁	—	2	4	no	—
135	C₂×C₄²×C₃₁	—	2	2	no	—
136	C₂×C₄²×C₃₁	—	2	1	no	—
137	C₂×C₄²×C₃₁	—	4	2	no	—
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊C₈	—	2	1	no	—
143	C₃₁×C₄⋊C₈	—	2	1	no	—
144	C₃₁×#104	—	2	4	no	—
145	C₃₁×#104	—	2	2	no	—
146	C₃₁×#104	—	2	4	no	—
147	C₃₁×#104	—	2	4	no	—
148	C₃₁×#104	—	4	2	no	—
149	C₃₁×#104	—	4	2	no	—
150	C₃₁×#104	D₄	1	4	yes	direct product factor
151	C₃₁×C₂²⋊C₈	—	2	2	no	—
152	C₃₁×C₂²⋊C₈	—	2	2	no	—
153	C₃₁×#97	—	2	1	no	—
154	C₄×C₈×C₃₁	—	2	1	no	—
155	C₃₁×#95	—	2	1	no	—
156	C₃₁×#95	—	2	2	no	—
157	C₂⁴×C₃₁	—	2	2	no	—
158	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
159	#41×C₃₁	—	2	1	no	—
160	#41×C₃₁	—	2	1	no	—
161	#41×C₃₁	—	2	4	no	—
162	#41×C₃₁	—	2	4	no	—
163	#41×C₃₁	—	2	2	no	—
164	#41×C₃₁	—	2	2	no	—
165	#41×C₃₁	—	2	2	no	—
166	#41×C₃₁	—	2	2	no	—
167	#41×C₃₁	—	4	4	no	—
168	#41×C₃₁	—	4	4	no	—
169	#41×C₃₁	—	4	2	no	—
170	#41×C₃₁	—	4	2	no	—
171	#41×C₃₁	—	4	4	no	—
172	#41×C₃₁	—	4	4	no	—
173	#41×C₃₁	C₂×D₄	1	2	yes	—
174	#41×C₃₁	#41	1	2	yes	—
175	C₂×Q₈×C₃₁	—	2	2	no	—
176	C₂×Q₈×C₃₁	—	2	4	no	—
177	C₂×Q₈×C₃₁	—	4	2	no	—
178	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
179	C₂×Q₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₃₁	—	2	1	no	—
181	C₂×D₄×C₃₁	—	2	4	no	—
182	C₂×D₄×C₃₁	—	2	4	no	—
183	C₂×D₄×C₃₁	—	2	2	no	—
184	C₂×D₄×C₃₁	—	2	2	no	—
185	C₂×D₄×C₃₁	—	2	2	no	—
186	C₂×D₄×C₃₁	—	2	2	no	—
187	C₂×D₄×C₃₁	—	2	2	no	—
188	C₂×D₄×C₃₁	—	2	1	no	—
189	C₂×D₄×C₃₁	—	2	2	no	—
190	C₂×D₄×C₃₁	—	2	1	no	—
191	C₂×D₄×C₃₁	—	4	2	no	—
192	C₂×D₄×C₃₁	—	4	4	no	—
193	C₂×D₄×C₃₁	—	4	4	no	—
194	C₂×D₄×C₃₁	—	4	4	no	—
195	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
196	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×D₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
199	C₂×D₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	—	2	1	no	—
201	C₂²×C₄×C₃₁	—	2	2	no	—
202	C₂²×C₄×C₃₁	—	2	1	no	—
203	C₂²×C₄×C₃₁	—	2	2	no	—
204	C₂²×C₄×C₃₁	—	2	2	no	—
205	C₂²×C₄×C₃₁	—	2	2	no	—
206	C₂²×C₄×C₃₁	—	2	8	no	—
207	C₂²×C₄×C₃₁	—	2	2	no	—
208	C₂²×C₄×C₃₁	—	2	1	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	1	no	—
211	C₂²×C₄×C₃₁	—	2	2	no	—
212	C₂²×C₄×C₃₁	—	2	2	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	1	no	—
215	C₂²×C₄×C₃₁	—	4	4	no	—
216	C₂²×C₄×C₃₁	—	4	4	no	—
217	C₂²×C₄×C₃₁	—	4	4	no	—
218	C₂²×C₄×C₃₁	—	4	4	no	—
219	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
220	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
227	M₁₆×C₃₁	—	2	1	no	—
228	M₁₆×C₃₁	—	2	2	no	—
229	M₁₆×C₃₁	—	2	1	no	—
230	M₁₆×C₃₁	—	2	1	no	—
231	M₁₆×C₃₁	—	2	2	no	—
232	M₁₆×C₃₁	—	4	4	no	—
233	M₁₆×C₃₁	C₂×D₄	1	2	yes	complemented
234	C₂×C₈×C₃₁	—	2	1	no	—
235	C₂×C₈×C₃₁	—	2	1	no	—
236	C₂×C₈×C₃₁	—	2	2	no	—
237	C₂×C₈×C₃₁	—	4	4	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	1	no	—
240	C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₄⋊C₄×C₃₁	—	2	1	no	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
246	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
247	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
248	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₃₁	—	2	8	no	—
251	C₂²⋊C₄×C₃₁	—	2	2	no	—
252	C₂²⋊C₄×C₃₁	—	2	2	no	—
253	C₂²⋊C₄×C₃₁	—	2	1	no	—
254	C₂²⋊C₄×C₃₁	—	2	2	no	—
255	C₂²⋊C₄×C₃₁	—	2	2	no	—
256	C₂²⋊C₄×C₃₁	—	2	1	no	—
257	C₂²⋊C₄×C₃₁	—	2	1	no	—
258	C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
261	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
262	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
263	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
264	C₄²×C₃₁	—	2	4	no	—
265	C₄²×C₃₁	—	2	1	no	—
266	C₄²×C₃₁	—	2	1	no	—
267	C₄²×C₃₁	—	2	1	no	—
268	C₄²×C₃₁	—	2	1	no	—
269	C₄²×C₃₁	—	2	2	no	—
270	C₄²×C₃₁	—	2	1	no	—
271	C₄²×C₃₁	—	2	1	no	—
272	C₄²×C₃₁	—	2	2	no	—
273	C₄²×C₃₁	—	4	4	no	—
274	C₄²×C₃₁	—	4	2	no	—
275	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
276	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₃₁	C₂×D₄	1	2	yes	complemented
280	D₄×#104	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂³×C₃₁	—	2	1	no	—
282	C₂³×C₃₁	—	2	2	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	4	no	—
285	C₂³×C₃₁	—	2	2	no	—
286	C₂³×C₃₁	—	4	2	no	—
287	C₂³×C₃₁	—	4	4	no	—
288	C₂³×C₃₁	—	4	4	no	—
289	C₂³×C₃₁	—	8	2	no	—
290	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₃₁	—	2	1	no	—
294	Q₈×C₃₁	—	2	2	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	4	4	no	—
297	Q₈×C₃₁	C₄×D₄	1	2	yes	complemented
298	D₄×C₃₁	—	2	2	no	—
299	D₄×C₃₁	—	2	2	no	—
300	D₄×C₃₁	—	2	4	no	—
301	D₄×C₃₁	—	2	2	no	—
302	D₄×C₃₁	—	2	1	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	4	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	8	1	no	—
313	D₄×C₃₁	—	8	2	no	—
314	D₄×C₃₁	#104	1	4	yes	direct product factor
315	D₄×C₃₁	C₄×D₄	1	2	yes	complemented
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	1	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	4	1	no	—
339	C₂×C₄×C₃₁	—	4	4	no	—
340	C₂×C₄×C₃₁	—	4	4	no	—
341	C₂×C₄×C₃₁	—	4	4	no	—
342	C₂×C₄×C₃₁	—	4	16	no	—
343	C₂×C₄×C₃₁	—	4	1	no	—
344	C₂×C₄×C₃₁	—	4	2	no	—
345	C₂×C₄×C₃₁	—	4	2	no	—
346	C₂×C₄×C₃₁	—	4	1	no	—
347	C₂×C₄×C₃₁	—	4	2	no	—
348	C₂×C₄×C₃₁	—	4	2	no	—
349	C₂×C₄×C₃₁	—	4	2	no	—
350	C₂×C₄×C₃₁	—	8	1	no	—
351	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₃₁	—	2	2	no	—
364	C₈×C₃₁	—	4	2	no	—
365	C₈×C₃₁	—	4	1	no	—
366	D₄×#41	C₂×C₃₁	1	1	yes	characteristic
367	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
368	C₂²×#104	C₂×C₃₁	1	2	yes	complemented
369	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#1980	C₂×C₃₁	1	1	yes	characteristic, complemented
371	#1962	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#1896	C₂×C₃₁	1	2	yes	complemented
373	#1871	C₂×C₃₁	1	2	yes	complemented
374	#1806	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#1789	C₂×C₃₁	1	2	yes	complemented
376	C₄×#104	C₂×C₃₁	1	1	yes	characteristic, complemented
377	C₂²×C₃₁	—	2	2	no	—
378	C₂²×C₃₁	—	2	1	no	—
379	C₂²×C₃₁	—	2	1	no	—
380	C₂²×C₃₁	—	2	2	no	—
381	C₂²×C₃₁	—	2	2	no	—
382	C₂²×C₃₁	—	2	2	no	—
383	C₂²×C₃₁	—	2	2	no	—
384	C₂²×C₃₁	—	2	2	no	—
385	C₂²×C₃₁	—	4	4	no	—
386	C₂²×C₃₁	—	4	4	no	—
387	C₂²×C₃₁	—	4	1	no	—
388	C₂²×C₃₁	—	4	1	no	—
389	C₂²×C₃₁	—	4	2	no	—
390	C₂²×C₃₁	—	4	2	no	—
391	C₂²×C₃₁	—	4	2	no	—
392	C₂²×C₃₁	—	8	8	no	—
393	C₂²×C₃₁	C₂×#104	1	4	yes	complemented
394	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₃₁	D₄²	1	1	yes	characteristic
396	C₂²×C₃₁	#546	1	1	yes	characteristic
397	C₄×C₃₁	—	2	4	no	—
398	C₄×C₃₁	—	2	2	no	—
399	C₄×C₃₁	—	2	2	no	—
400	C₄×C₃₁	—	2	2	no	—
401	C₄×C₃₁	—	2	1	no	—
402	C₄×C₃₁	—	2	1	no	—
403	C₄×C₃₁	—	2	1	no	—
404	C₄×C₃₁	—	4	2	no	—
405	C₄×C₃₁	—	4	4	no	—
406	C₄×C₃₁	—	4	2	no	—
407	C₄×C₃₁	—	4	1	no	—
408	C₄×C₃₁	—	4	1	no	—
409	C₄×C₃₁	C₂×#104	1	2	yes	complemented
410	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
411	C₄×C₃₁	#518	1	1	yes	characteristic
412	C₄×C₃₁	D₄²	1	1	yes	characteristic
413	C₄×C₃₁	#546	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₃₁	1	2	yes	—
415	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
416	#550	C₄×C₃₁	1	1	yes	characteristic, complemented
417	D₄×Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
418	#548	C₄×C₃₁	1	2	yes	complemented
419	#547	—	2	1	no	—
420	#547	C₄×C₃₁	1	1	yes	characteristic, complemented
421	#546	—	2	2	no	—
422	#546	C₄×C₃₁	1	2	yes	complemented
423	D₄²	—	2	1	no	—
424	D₄²	C₄×C₃₁	1	1	yes	characteristic, complemented
425	#532	—	2	1	no	—
426	#532	C₂²×C₃₁	1	1	yes	characteristic
427	#525	—	2	2	no	—
428	#525	C₂²×C₃₁	1	2	yes	—
429	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₄×D₄	—	2	1	no	—
431	C₂×C₄×D₄	—	2	1	no	—
432	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
433	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
434	#436	—	2	1	no	—
435	#435	—	2	2	no	—
436	C₈×D₄	—	2	1	no	—
437	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	C₂×#104	—	2	8	no	—
439	C₂×#104	C₂²×C₃₁	1	2	yes	—
440	C₂×#104	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×#104	C₂²×C₃₁	1	1	yes	characteristic
442	C₂×#104	C₂²×C₃₁	1	2	yes	complemented
443	C₂×#104	C₂²×C₃₁	1	2	yes	complemented
444	C₂×#104	C₂²×C₃₁	1	2	yes	complemented
445	C₂×#104	C₂²×C₃₁	1	2	yes	complemented
446	#407	C₂²×C₃₁	1	2	yes	complemented
447	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
448	C₄×C₄⋊C₄	—	2	1	no	—
449	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	C₄×C₂²⋊C₄	—	2	2	no	—
451	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
452	C₄³	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	#339	C₂²×C₃₁	1	2	yes	complemented
454	#339	C₂²×C₃₁	1	1	yes	characteristic, complemented
455	#339	C₂²×C₃₁	1	1	yes	characteristic, complemented
456	C₂×C₃₁	—	2	1	no	—
457	C₂×C₃₁	—	2	1	no	—
458	C₂×C₃₁	—	2	4	no	—
459	C₂×C₃₁	—	4	2	no	—
460	C₂×C₃₁	—	4	2	no	—
461	C₂×C₃₁	—	8	2	no	—
462	C₂×C₃₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
464	C₂×C₃₁	#2901	1	1	yes	characteristic
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	4	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	4	2	no	—
470	C₂×#41	—	4	2	no	—
471	C₂×#41	C₂×C₄×C₃₁	1	2	yes	complemented
472	C₂×#41	C₂×C₄×C₃₁	1	2	yes	complemented
473	C₂×#41	C₂³×C₃₁	1	2	yes	—
474	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
475	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	complemented
479	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
480	C₂³×C₄	—	2	2	no	—
481	C₂³×C₄	—	2	2	no	—
482	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
483	C₂×M₁₆	—	2	2	no	—
484	C₂×M₁₆	—	2	4	no	—
485	C₂×M₁₆	—	4	2	no	—
486	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
487	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
492	#127	—	2	1	no	—
493	#127	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
494	#124	—	2	2	no	—
495	#124	C₂×C₄×C₃₁	1	2	yes	complemented
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
502	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
503	#121	—	2	2	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	C₂×C₄×C₃₁	1	2	yes	complemented
511	#121	C₂×C₄×C₃₁	1	2	yes	complemented
512	#120	—	2	2	no	—
513	#120	—	2	2	no	—
514	#120	—	2	2	no	—
515	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
516	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
528	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
529	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
530	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
531	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic, complemented
532	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
533	C₄×D₄	D₄×C₃₁	1	2	yes	—
534	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
535	#117	—	2	1	no	—
536	#117	C₂³×C₃₁	1	1	yes	characteristic
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	—	2	4	no	—
546	C₂×C₄²	—	2	1	no	—
547	C₂×C₄²	—	2	2	no	—
548	C₂×C₄²	—	4	2	no	—
549	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
553	C₄⋊C₈	—	2	1	no	—
554	C₄⋊C₈	—	2	1	no	—
555	#104	—	2	4	no	—
556	#104	—	2	2	no	—
557	#104	—	2	4	no	—
558	#104	—	2	4	no	—
559	#104	—	4	2	no	—
560	#104	—	4	2	no	—
561	#104	D₄×C₃₁	1	4	yes	direct product factor
562	C₂²⋊C₈	—	2	2	no	—
563	C₂²⋊C₈	—	2	2	no	—
564	#97	—	2	1	no	—
565	C₄×C₈	—	2	1	no	—
566	#95	—	2	1	no	—
567	#95	—	2	2	no	—
568	C₃₁	D₄×#104	1	1	yes	characteristic, direct product factor, Sylow
569	C₂⁴	—	2	2	no	—
570	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
571	#41	—	2	1	no	—
572	#41	—	2	1	no	—
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	#41	—	4	2	no	—
582	#41	—	4	2	no	—
583	#41	—	4	4	no	—
584	#41	—	4	4	no	—
585	#41	C₂×D₄×C₃₁	1	2	yes	—
586	#41	#41×C₃₁	1	2	yes	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
591	C₂×Q₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
608	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
609	C₂×D₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
610	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
611	C₂×D₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	—	4	4	no	—
631	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
632	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
633	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
636	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
639	M₁₆	—	2	1	no	—
640	M₁₆	—	2	2	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	1	no	—
643	M₁₆	—	2	2	no	—
644	M₁₆	—	4	4	no	—
645	M₁₆	C₂×D₄×C₃₁	1	2	yes	complemented
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	2	no	—
649	C₂×C₈	—	4	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
658	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
659	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
660	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
661	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
673	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
674	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
675	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	4	4	no	—
686	C₄²	—	4	2	no	—
687	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
688	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
691	C₄²	C₂×D₄×C₃₁	1	2	yes	complemented
692	C₂³	—	2	4	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
702	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
703	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	4	no	—
708	Q₈	C₄×D₄×C₃₁	1	2	yes	complemented
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	2	no	—
725	D₄	C₃₁×#104	1	4	yes	direct product factor
726	D₄	C₄×D₄×C₃₁	1	2	yes	complemented
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
763	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
764	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
765	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
766	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
767	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
768	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
771	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
772	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
774	C₈	—	2	2	no	—
775	C₈	—	4	2	no	—
776	C₈	—	4	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	8	no	—
793	C₂²	C₂×C₃₁×#104	1	4	yes	complemented
794	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
795	C₂²	D₄²×C₃₁	1	1	yes	characteristic
796	C₂²	C₃₁×#546	1	1	yes	characteristic
797	C₄	—	2	4	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	C₂×C₃₁×#104	1	2	yes	complemented
810	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
811	C₄	C₃₁×#518	1	1	yes	characteristic
812	C₄	D₄²×C₃₁	1	1	yes	characteristic
813	C₄	C₃₁×#546	1	1	yes	characteristic
814	C₂	—	2	1	no	—
815	C₂	—	2	1	no	—
816	C₂	—	2	4	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	D₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
821	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic
822	C₂	C₃₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
prime radical	D₄×#41×C₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. D₄×M₁₆×C₃₁	C₂	semidirect
3. C₂²×C₃₁×#104	C₂	semidirect
4. C₄²×D₄×C₃₁	C₂	semidirect
5. C₃₁×#1980	C₂	semidirect
6. C₃₁×#1962	C₂	semidirect
7. C₃₁×#1896	C₂	semidirect
8. C₃₁×#1871	C₂	semidirect
9. C₃₁×#1806	C₂	semidirect
10. C₃₁×#1789	C₂	semidirect
11. C₄×C₃₁×#104	C₂	semidirect
13. C₂²×M₁₆×C₃₁	C₂²	semidirect
14. C₃₁×#550	C₄	semidirect
15. D₄×Q₈×C₃₁	C₄	semidirect
16. C₃₁×#548	C₄	semidirect
18. C₃₁×#547	C₄	semidirect
20. C₃₁×#546	C₄	semidirect
22. D₄²×C₃₁	C₄	semidirect
31. C₂²×C₄²×C₃₁	C₂²	semidirect
35. C₃₁×#423	C₂²	semidirect
40. C₂×C₃₁×#104	C₂²	semidirect
41. C₂×C₃₁×#104	C₂²	semidirect
42. C₂×C₃₁×#104	C₂²	semidirect
43. C₂×C₃₁×#104	C₂²	semidirect
44. C₃₁×#407	C₂²	semidirect
45. C₄×M₁₆×C₃₁	C₂²	semidirect
47. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
50. C₄³×C₃₁	C₂²	semidirect
51. C₃₁×#339	C₂²	semidirect
52. C₃₁×#339	C₂²	semidirect
53. C₃₁×#339	C₂²	semidirect
60. C₂×#41×C₃₁	C₂×C₄	semidirect
61. C₂×#41×C₃₁	C₂×C₄	semidirect
64. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
67. C₂²×D₄×C₃₁	C₂×C₄	semidirect
80. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
82. C₃₁×#127	C₂×C₄	semidirect
84. C₃₁×#124	C₂×C₄	semidirect
90. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₃₁×#121	C₂×C₄	semidirect
100. C₃₁×#121	C₂×C₄	semidirect
104. C₄×Q₈×C₃₁	C₂×C₄	semidirect
105. C₄×Q₈×C₃₁	C₂×C₄	semidirect
119. C₄×D₄×C₃₁	C₂×C₄	semidirect
120. C₄×D₄×C₃₁	C₂×C₄	semidirect
150. C₃₁×#104	D₄	direct (N × H)
233. M₁₆×C₃₁	C₂×D₄	semidirect
279. C₄²×C₃₁	C₂×D₄	semidirect
280. D₄×#104	C₃₁	direct (N × H)
297. Q₈×C₃₁	C₄×D₄	semidirect
314. D₄×C₃₁	#104	direct (N × H)
315. D₄×C₃₁	C₄×D₄	semidirect
367. D₄×M₁₆	C₂×C₃₁	semidirect
368. C₂²×#104	C₂×C₃₁	semidirect
369. C₄²×D₄	C₂×C₃₁	semidirect
370. #1980	C₂×C₃₁	semidirect
371. #1962	C₂×C₃₁	semidirect
372. #1896	C₂×C₃₁	semidirect
373. #1871	C₂×C₃₁	semidirect
374. #1806	C₂×C₃₁	semidirect
375. #1789	C₂×C₃₁	semidirect
376. C₄×#104	C₂×C₃₁	semidirect
393. C₂²×C₃₁	C₂×#104	semidirect
409. C₄×C₃₁	C₂×#104	semidirect
415. C₂²×M₁₆	C₂²×C₃₁	semidirect
416. #550	C₄×C₃₁	semidirect
417. D₄×Q₈	C₄×C₃₁	semidirect
418. #548	C₄×C₃₁	semidirect
420. #547	C₄×C₃₁	semidirect
422. #546	C₄×C₃₁	semidirect
424. D₄²	C₄×C₃₁	semidirect
433. C₂²×C₄²	C₂²×C₃₁	semidirect
437. #423	C₂²×C₃₁	semidirect
442. C₂×#104	C₂²×C₃₁	semidirect
443. C₂×#104	C₂²×C₃₁	semidirect
444. C₂×#104	C₂²×C₃₁	semidirect
445. C₂×#104	C₂²×C₃₁	semidirect
446. #407	C₂²×C₃₁	semidirect
447. C₄×M₁₆	C₂²×C₃₁	semidirect
449. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
451. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
452. C₄³	C₂²×C₃₁	semidirect
453. #339	C₂²×C₃₁	semidirect
454. #339	C₂²×C₃₁	semidirect
455. #339	C₂²×C₃₁	semidirect
471. C₂×#41	C₂×C₄×C₃₁	semidirect
472. C₂×#41	C₂×C₄×C₃₁	semidirect
475. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
478. C₂²×D₄	C₂×C₄×C₃₁	semidirect
491. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
493. #127	C₂×C₄×C₃₁	semidirect
495. #124	C₂×C₄×C₃₁	semidirect
501. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
502. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
510. #121	C₂×C₄×C₃₁	semidirect
511. #121	C₂×C₄×C₃₁	semidirect
515. C₄×Q₈	C₂×C₄×C₃₁	semidirect
516. C₄×Q₈	C₂×C₄×C₃₁	semidirect
530. C₄×D₄	C₂×C₄×C₃₁	semidirect
531. C₄×D₄	C₂×C₄×C₃₁	semidirect
561. #104	D₄×C₃₁	direct (N × H)
568. C₃₁	D₄×#104	direct (N × H)
645. M₁₆	C₂×D₄×C₃₁	semidirect
691. C₄²	C₂×D₄×C₃₁	semidirect
708. Q₈	C₄×D₄×C₃₁	semidirect
725. D₄	C₃₁×#104	direct (N × H)
726. D₄	C₄×D₄×C₃₁	semidirect
793. C₂²	C₂×C₃₁×#104	semidirect
809. C₄	C₂×C₃₁×#104	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×#41×C₃₁	2
D₄×M₁₆×C₃₁	2
C₂²×C₃₁×#104	2
C₄²×D₄×C₃₁	2
C₃₁×#1980	2
C₃₁×#1962	2
C₃₁×#1896	2
C₃₁×#1871	2
C₃₁×#1806	2
C₃₁×#1789	2
C₄×C₃₁×#104	2
D₄×#104	31

Subgroups — D4×C31×#104 #21479192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃₁×#104 #21479192